The IIT Madras BS Statistics for Data Science I (Stats 1) End Term paper sat on 3 Apr 2022, in the January 2022 term: 15 questions for 50 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Six students are randomly selected from the top 15 students of a class to find if their overall score is affected by their response to the first question in the exam. Based on the data given in Table Q.1, answer the subquestions.
Calculate the absolute value of Point Bi-serial correlation coefficient between the response to the first question and overall-marks obtained by the students. (Enter the answer correct to 2 decimal places)
Correct answer: 0.82 (accepted within ±0.05)
Six students are randomly selected from the top 15 students of a class to find if their overall score is affected by their response to the first question in the exam. Based on the data given in Table Q.1, answer the subquestions.
Are the overall-marks obtained by the selected students strongly influenced by their response to the first question in the exam?
Yes, because the absolute value of Point Bi-serial correlation coefficient is greater than 0.75.
No, because the absolute value of Point Bi-serial correlation coefficient is greater than 0.75.
Yes, because the absolute value of Point Bi-serial correlation coefficient is less than 0.75.
No, because the absolute value of Point Bi-serial correlation coefficient is less than 0.75.
Correct answer
Yes, because the absolute value of Point Bi-serial correlation coefficient is greater than 0.75.
In a manufacturing company, which produces medicine bottles, the chance that the bottles are of good quality is 60%, independent of each other. A sample of 5 bottles is selected for a quality inspection. Based on the given information, answer the subquestions.
What is the probability that exactly 4 bottles are of good quality, given that at least 1 bottle is of good quality?(Enter the answer correct to 2 decimal places)
Correct answer: 0.26 (accepted within ±0.04)
In a manufacturing company, which produces medicine bottles, the chance that the bottles are of good quality is 60%, independent of each other. A sample of 5 bottles is selected for a quality inspection. Based on the given information, answer the subquestions.
If the random variable X denotes the number of good quality bottles selected, then calculate the Var(X)?
NOTE: Enter your answer in two decimal places.
Correct answer: 1.2 (accepted within ±0.01)
Number of attempts to score a goal by the players in a football match is represented by a Box plot as shown in Fig Q.1.
Which of the following statements is/are correct?
Approximately 50% of players attempted 2 to 8 shots to score a goal in a football match.
Approximately 50% of players attempted 8 to 18 shots to score a goal in a football match.
Approximately 50% of players attempted 5 to 14 shots to score a goal in a football match.
Range of the dataset is 9.
Range of the dataset is 16.
Correct answers
Approximately 50% of players attempted 2 to 8 shots to score a goal in a football match.
Approximately 50% of players attempted 8 to 18 shots to score a goal in a football match.
Approximately 50% of players attempted 5 to 14 shots to score a goal in a football match.
Range of the dataset is 16.
Which of the following option(s) is/are incorrect for a variable having interval scale of measurement?
Difference between the values of a variable can be evaluated.
Order of the data is meaningful.
Multiplication and division of values of a variable is possible.
It has an absolute zero.
Correct answers
Multiplication and division of values of a variable is possible.
It has an absolute zero.
There are 5 distinct bags and 4 balls of different colors. In how many ways can the balls be put in bags such that there are exactly 2 balls in exactly one of the bags?
480
360
180
720
Correct answer
360
A biased coin, with probability of tails 0.2, is tossed repeatedly and independently until the first head is observed. Find the probability that the first head appears at an even numbered toss.
Correct answer
Sumit wants to contact one of his friends, but he remembers only the first 9 of the 10 digits of the contact number. He is sure that the last digit of the contact number is an even number. He selects an even number randomly. If the random variable X denotes the last digit of the contact number, then calculate Var(X).
4
8
24
None of these
Correct answer
8
At a certain university, 10% of men are over 6 feet tall and 5% of women are over 6 feet tall. The total student population is divided in the ratio 4:3 in favor of women. If a randomly selected student is over six feet tall, then what is the probability that the student is a woman?(Enter the answer correct to 2 decimal places)
Correct answer: 0.4 (accepted within ±0.04)
A box contains 7 items out of which 2 are defective. A sample of 4 items is to be selected randomly (without replacement) from the box. If the random variable X represents the number of defective items in a selection of 4 items, then find E(X).(Enter the answer correct to 2 decimal places)
Correct answer: 1.14 (accepted within ±0.04)
A random variable X has the following probability mass function:
Based on the information given in Table Q.2, answer the subquestions.
What is the value of P(1 < X < 5)?
Correct answer
A random variable X has the following probability mass function:
Based on the information given in Table Q.2, answer the subquestions.
Correct answer
Kanika has to catch a train to go to her hometown, and the time to pass the security screening at the railway station follows exponential distribution. It is noted that the mean time to pass through the security screening is 10 minutes. To catch the train, Kanika must clear the security screening within 10 minutes. What is the probability that Kanika will miss the train?
e^(−1)
1 − e^(−1)
e^(−10)
1 − e^(−10)
Correct answer
e^(−1)
Suppose a 20 year-old student takes time uniformly between 5 to 15 minutes to read a newspaper. If X denotes the time (in minutes) taken by a student to read a newspaper, then find the probability that a randomly selected 20 year old student needs at most 12 minutes to read a newspaper?
Correct answer
